The HR system is a piece of software that automatically creates mathematical concepts and discovers conjectures about them. The system is now capable of generating and testing the solvability of puzzles within wide constraints, and we’ve developed a set of puzzles we’re calling Donatsu (transliterated Japanese for “Doughnut”). These involve the player following a loop (or various other loop-like designs) attempting to get a series of numbers to reach particular totals through adding mathematical operators (+, -, /, and x).

I've pasted in below four of the many permutations we've developed - Uninatsu (the most basic), Chromanatsu, Maxinatsu, and Hexanatsu (the most complex) - alongside appropriate instructions. You can also download to print off a paper version, since these are paper puzzles, after all! Our long-term goal is to develop and refine these to the point that we can potentially get some published in newspapers.

So: we'd love to get your feedback! Aside from the obvious - are these fun and interesting to solve - we'd also like to ask two main questions: 1) which did you like most, and why, and 2) what would you improve about the puzzles? This is still the early stage of development, so we're trying to pin down the best puzzle permutations possible. Thanks!